How would I construct a circuit similar to a differential op amp but I ALWAYS want the output to be positive.
So for example V1=non-inverting pin and V=inverting pin
When V1 is 1.5V and V2 is 3V I want Vout to be 1.5V
Then if V1 is 3V and V2 is 1.5V I want Vout to still be 1.5V

An instrumentation amplifier followed by a Precision Rectifier. Use google for links. But this one is one of the best http://sound.westhost.com/appnotes/an001.htm
You did not say anything about bandwidth. Most of the Precision Rectifier circuits will work fine up to around 100 KHz at least. Above that it may be harder to find a proper solution